A new approach to the analytical implementation of the Rosenblatt transformation is described. It leverages the properties of the empirical probability density function, which is the standard estimate of an unknown density. As such its utility is to applications where training data is available for the unknown density. These applications include data-driven algorithms for detection/classification and other statistical signal processing problems where the underlying probabilistic description of the data is unknown. As an illustration, an application to anomaly detection is described in detail using Gaussian and radar datasets.

A classification rule based on the cumulant generating function of the training data, called the Cumulant Generating Function Classifier (CGFC), has been recently proposed, and has shown promising performance in terms of improved classification accuracy and robustness against noises. This paper first presents a new information-theoretical explanation of CGFC which indeed makes a classification by minimizing sample mutual information. The original CGFC is a type of global model, and a new variant, called Local-CGFC, is further introduced in this paper to achieve a local classification rule. Experimental studies on real-life datasets demonstrate the effectiveness of the proposed classifier and further illustrate its great potential for a number of real-world applications.

Detection of known signals of interest that are embedded in colored noise involves whitening the received samples and matched-filtering. In many applications, due to computational constraints, it is critical to select only a subset of the received samples for detection. This paper addresses the problem of selecting only a given number of temporal or spatial samples while maximizing detection performance for deterministic signals in first-order autoregressive Gaussian noise. The direct solution of this entails a combinatorial search, where the deflection coefficient is evaluated for each possible combination of sparse samples. This approach is infeasible when the number of samples is large since the number of possible combinations increases factorially with the number of samples. We present an efficient method to whiten Gaussian noise samples and express deflection coefficient in a form that is amenable to dynamic programming. Exploiting dynamic programming, we specify a feasible and efficient procedure to find optimal sparse samples where the number of computational steps increases linearly with the number of samples. Also, conditions under which uniform sampling is optimal is given.

The problem of detecting an anomaly based on two sets of data, the first one that is assumed to represent a quiescent condition, and the second that may contain an anomaly, is addressed. Using estimated mutual information as a discriminating indicator of change, a detector is configured and interpreted, with the changing parameter modeled as the outcome of a random variable. The relationship of the proposed detector to the standard generalized likelihood ratio test is also examined. It is found that the resulting approach merges concepts in information theory, for which a Bayesian assumption is made for the underlying change parameter, with classical decision theory, for which a frequentist assumption for the change parameter is utilized.

A new approach to the problem of dimensionality reduction is proposed. The specific application is to the detection of signals in noise, although it should be applicable to other signal processing problems of current interest. Using a minimum mean square error estimator of the likelihood ratio one can determine a low dimensional statistic, not necessarily linear in the data, that performs well for detection, i.e., with minimal loss of information. If a sufficient statistic does exist for the problem then the proposed approach yields the well known result that one should use the likelihood ratio of the sufficient statistic for detection. Other interesting relationships are explored and some specific examples are given.

We address the problem of sparse sampling pattern design to maximize detection for a deterministic signal in colored noise. We model a colored noise as a continuous-time autoregressive process, which is obtained by passing a white noise through a causal linear-time invariant filter. This noise modeling is crucial to the development of the optimal sampling pattern design for a given number of sensors. We obtain a closed form expression for the whitening filter and consequently, for the Kullback-Leibler divergence at the whitening filter output, which is the detection index. The optimum sampling pattern is obtained by evaluating the detection index at Nyquist sampling rate, rank ordering the samples, and selecting the maximum values. We present some examples to illustrate the proposed procedure. We also extend our method to two-dimensional sampling. The advantage of our approach is its low computational complexity for both one-dimensional and two-dimensional cases and that optimality is guaranteed.

A means of converting a random variable into an approximate standard normal is described. It is an extension of the transformation inherent in the use of the exponential embedded family approach to multifamily likelihood ratio testing, which helps explain why the transformation employed corrects the deficiencies of the generalized likelihood ratio test.

In this letter, we investigate the problem of radar signal waveform design under the small signal power conditions for detecting a doubly spread target in colored noise. The doubly spread target is range spread and its impulse response is time varying due to fluctuation (hence Doppler spread). The locally most powerful detector is derived for detecting such targets. The signal waveform is optimized to maximizing the detector's detection performance or equivalently the Kullback-Leibler divergence. Numerical simulations validate the effectiveness of the proposed waveform design by comparing it with the frequency modulated (LFM) waveform.

The penalty term plays an important role in model order selection rules. The Exponentially Embedded Families (EEF) is consistent and effective in model order selection. In this paper we show that the EEF penalty term can be viewed as estimated mutual information (MI) between unknown parameters and received data from Bayesian viewpoints. The finding is a result of an important relationship between Kullback-Leibler Divergence (KLD), signal-to-noise ratio (SNR) and MI in estimation/detection of random signals, which is also introduced.

In this letter, we address the problem of designing the optimal radar waveform for the detection of an extended target in a colored noise environment. The locally most powerful detector and the corresponding optimal waveform based on maximizing the detector's performance under a small-signal assumption are derived. The performance is evaluated analytically, and numerically compared with that of the mutual information based method. The locally most powerful detection metric is shown to be the Kullback-Leibler divergence. The use of the latter measure leads to a substantial performance improvement. Moreover, a useful relationship among the three existing waveform design metrics, namely the output signal-to-noise ratio, the Kullback-Leibler divergence, and the mutual information, is provided. It explains the tradeoffs of the various metrics currently used for radar waveform design.

Banding the inverse of covariance matrix has become a popular technique to estimate a high dimensional covariance matrix from limited number of samples. However, little work has been done in providing a criterion to determine when a matrix is bandable. In this paper, we present a detector to test the bandedness of a Cholesky factor matrix. The test statistic is formed based on the Rao test, which does not require the maximum likelihood estimates under the alternative hypothesis. In many fields, such as radar signal processing, the covariance matrix and its unknown parameters are often complex-valued. We focus on dealing with complex-valued cases by utilizing the complex parameter Rao test, instead of the traditional real Rao test. This leads to a more intuitive and efficient test statistic. Examples and computer simulations are given to investigate the derived detector performance.

In this paper, we present a novel exponentially embedded families (EEF) based classification method, in which the probability density function (PDF) on raw data is estimated from the PDF on features. With the PDF construction, we show that class-specific features can be used in the proposed classification method, instead of a common feature subset for all classes as used in conventional approaches. We apply the proposed EEF classifier for text categorization as a case study and derive an optimal Bayesian classification rule with class-specific feature selection based on the Information Gain score. The promising performance on real-life data sets demonstrates the effectiveness of the proposed approach and indicates its wide potential applications.

In this paper, we present a Bayesian classification approach for automatic text categorization using class-specific features. Unlike conventional text categorization approaches, our proposed method selects a specific feature subset for each class. To apply these class-specific features for classification, we follow Baggenstoss's PDF Projection Theorem (PPT) to reconstruct the PDFs in raw data space from the class-specific PDFs in low-dimensional feature subspace, and build a Bayesian classification rule. One noticeable significance of our approach is that most feature selection criteria, such as Information Gain (IG) and Maximum Discrimination (MD), can be easily incorporated into our approach. We evaluate our method's classification performance on several real-world benchmarks, compared with the state-of-the-art feature selection approaches. The superior results demonstrate the effectiveness of the proposed approach and further indicate its wide potential applications in data mining.

Automated feature selection is important for text categorization to reduce feature size and to speed up learning process of classifiers. In this paper, we present a novel and efficient feature selection framework based on the Information Theory, which aims to rank the features with their discriminative capacity for classification. We first revisit two information measures: Kullback-Leibler divergence and Jeffreys divergence for binary hypothesis testing, and analyze their asymptotic properties relating to type I and type II errors of a Bayesian classifier. We then introduce a new divergence measure, called Jeffreys-Multi-Hypothesis (JMH) divergence, to measure multi-distribution divergence for multi-class classification. Based on the JMH-divergence, we develop two efficient feature selection methods, termed maximum discrimination ($MD$) and methods, for text categorization. The promising results of extensive experiments demonstrate the effectiveness of the proposed approaches.

The exponential mixture of probability mass functions arises in many fields. Although straightforward to characterize and utilize, it does not lead to a simple probabilistic interpretation as does the linear mixture. We remedy this by giving a general probabilistic problem whereby the exponential mixture describes the probabilities involved.

In this paper, we extend the exponentially embedded family (EEF), a new approach to model order estimation and probability density function construction originally proposed by Kay in 2005, to multivariate pattern recognition. Specifically, a parametric classifier rule based on the EEF is developed, in which we construct a distribution for each class based on a reference distribution. The proposed method can address different types of classification problems in either a data-driven manner or a model-driven manner. In this paper, we demonstrate its effectiveness with examples of synthetic data classification and real-life data classification in a data-driven manner and the example of power quality disturbance classification in a model-driven manner. To evaluate the classification performance of our approach, the Monte-Carlo method is used in our experiments. The promising experimental results indicate many potential applications of the proposed method.

The exponentially embedded family (EEF) of probability density functions was originally proposed in [1] for model order selection. The performance of the original EEF deteriorates somewhat when nuisance parameters are present, especially in the case of high signal-to-noise ratio (SNR). Therefore, we propose a new EEF for model order selection in the case of high SNR. It is shown that without nuisance parameters, the new EEF is the same as the original EEF. However, with nuisance parameters, the new EEF takes a different form. The new EEF is applied to problems of polynomial curve fitting and clustering. Simulation results show that, with nuisance parameters, the new EEF outperforms the original EEF and Bayesian information criterion (BIC) at high SNR.

The parametric classifiers trained with the Bayesian rule are usually more accurate than the non-parametric classifiers such as nearest neighbors, neural network and support vector machine, when the class-conditional densities of distribution models are known except for some of their parameters and the training data is abundant. However, the parametric classifiers would perform poorly if these class-conditional densities are unknown and the assumed distribution models are inaccurate. In this paper, we propose a hybrid classification method for the data with partially known distribution models where only the distribution models of some classes are known. For this partial models case, the proposed hybrid classifier makes the best use of knowledge of known distribution models with Bayesian interference, while both purely parametric and non-parametric classifiers would lose a specific predictive capacity for classification. Theoretical proofs and experimental results show that the proposed hybrid classifier has much better performance than these purely parametric and non-parametric classifiers for the data with partial models.

A method to obtain parameter estimates in a nonlinear least squares problem is proposed. Its main advantage is computational efficiency and can be used when a direct grid search cannot. The approach is based on the theory of random basis functions. An example of its application to frequency estimation is given and other applications discussed.

We consider a distributed detection problem where sensors are deployed to obtain information about a common source of interest. The centralized processing takes advantage of all sensor information, but requires more resources for data transmission and computation. On the other hand, independent processing requires less resources at a cost of some performance loss. In this letter, we analyze the performance of the generalized likelihood ratio test (GLRT) and the independent GLRT (IGLRT), and quantify the performance loss of the IGLRT. It is shown that the performance loss is due to an extra noise-like term with a chi-squared distribution which only depends on the dimensionality of the unknown parameterspand the number of sensorsM. The result is extended to a special scenario when sensors can communicate freely within the same group. Simulation results are provided to verify our analysis.

The Neyman-Pearson theorem for the problem of simple hypothesis testing provides the fundamental approach to signal detection. In this letter we present a new proof that leverages the properties of exponential probability density function families and furthermore links parameter estimation to detection, a point of contention between Neyman-Pearson and Fisher. The new proof also provides corollaries concerning known properties of the receiver operating characteristics. Finally, a geometric interpretation to the problem of signal detection is given, which can provide much insight into its solution.

A new paradigm for signal fitting is proposed. Unlike the customary approach in which fixed basis functions are used to represent the signal, the proposed method employs random basis functions. The advantage is an increase in robustness, leading to an overall decrease in modeling error. It also provides a new intepretation on the choice of regularization weightings for such applications as classification, spectral analysis, and adaptive beamforming. © 2006 IEEE.

The exponential embedding of two or more probability density functions (PDFs) is proposed for multimodal sensor processing. It approximates the unknown PDF by exponentially embedding the known PDFs. Such embedding is of a exponential family indexed by some parameters, and hence inherits many nice properties of the exponential family. It is shown that the approximated PDF is asymptotically the one that is the closest to the unknown PDF in Kullback-Leibler (KL) divergence. Applied to hypothesis testing, this approach shows improved performance compared to existing methods for cases of practical importance where the sensor outputs are not independent.

We describe a novel means of representing signals by a Fourier decomposition consisting of complex sinusoids with unit amplitudes and zero phases. The only information necessary to reconstruct the signal from its Fourier components consists of the “place” information, which specifies the sinusoidal frequencies to include in the synthesis. This set of frequencies results in a nonuniform distribution of sinusoidal frequency components. As such, the approach provides a means of representing a signal by a set of zeros and ones, indicating an off-on condition for each frequency component. It is conjectured that this might help explain the mechanism of auditory and visual neural encoding of acoustic and visual stimuli, respectively. As an immediate application of the theory, a classification experiment is conducted which indicates that the proposed neural encoding is more robust to noise than traditional approaches.

A proof of the pointwise convergence of the multidimensional minimum variance spectral estimator as the region of data support becomes infinite is given. It is shown that an octant is sufficient to ensure that the minimum variance spectral estimator will converge to the true power spectral density. The proof is valid for 1-D, multidimensional, continuous, and mixed spectra. Another useful result is that a normalized minimum variance spectral estimator can be defined to indicate sinusoidal power for processes with a mixed spectrum. Finally, upper and lower bounds on the continuous portion of the spectral estimate are given.

Online feedback-based rating systems are gaining popularity. Dealing with unfair ratings in such systems has been recognized as an important but difficult problem. This problem is challenging especially when the number of regular ratings is relatively small and unfair ratings can contribute to a significant portion of the overall ratings. Furthermore, the lack of unfair rating data from real human users is another obstacle toward realistic evaluation of defense mechanisms. In this paper, we propose a set of statistical methods to jointly detect collaborative unfair ratings in product-rating type online rating systems. Based on detection, a framework of trust-assisted rating aggregation system is developed. Furthermore, we collect unfair rating data from real human users through a rating challenge. The proposed system is evaluated through simulations as well as experiments using real attack data. Compared with existing schemes, the proposed system can significantly reduce negative impact from unfair ratings.

This paper investigates potential improvement of nonparametric detection performance via addition of noise and evaluates the performance of noise modified nonparametric detectors. Detection performance comparisons are made between the original detectors and noise modified detectors. Conditions for improvability as well as the optimum additive noise distributions of the widely used sign detector, the Wilcoxon detector, and the dead-zone limiter detector are derived. Finally, a simple and fast learning algorithm to find the optimal noise distribution solely based on received data is presented. A near-optimal solution can be found quickly based on a relatively small dataset.

It is shown in this letter that the addition of noise to data, resulting in noise enhanced detection, is equivalent to using a randomized decision rule. Since the theory of randomized decision-making is well developed, this link can be exploited to better understand the advantages, disadvantages, and general properties of noise enhanced detection. As an example, we show how some recent results can be interpreted within this more general framework.

Recently, the exponentially embedded families (EEF) criterion for model order selection has been proposed based on the theories of exponentially embedded families and sufficient statistics. In this letter, it is proved that the EEF criterion is consistent, and then the EEF is used to determine the number of sources in array signal processing. Computer simulation results demonstrate better performance of the EEF criterion for closely spaced sources, at low SNR and/or a small number of snapshots.

Stochastic-resonance (SR), a nonlinear physical phenomenon in which the performance of some nonlinear systems can be enhanced by adding suitable noise, has been observed and applied in many areas. However, it has not been shown whether or not this phenomenon plays a role in distributed detection. It seems counterintuitive that adding additional noise to the received decisions at the fusion center can improve detection performance. However, in this paper, we demonstrate the existence of the SR phenomenon in decision fusion by examples. An explanation for its existence is provided

This paper considers the stochastic resonance (SR) effect in the two hypotheses signal detection problem. Performance of a SR enhanced detector is derived in terms of the probability of detection PDand the probability of false alarm PFA. Furthermore, the conditions required for potential performance improvement using SR are developed. Expression for the optimal stochastic resonance noise pdf which renders the maximum po without increasing PFAis derived. By further strengthening the conditions, this approach yields the constant false alarm rate (CFAR) receiver. Finally, detector performance comparisons are made between the optimal SR noise, Gaussian, uniform and optimal symmetric pdf noises

The problem of reducing the probability of decision error of an existing binary receiver that is suboptimal using the ideas of stochastic resonance is solved. The optimal probability density function of the random variable that should be added to the input is found to be a Dirac delta function, and hence, the optimal random variable is a constant. The constant to be added depends upon the decision regions and the probability density functions under the two hypotheses and is illustrated with an example. Also, an approximate procedure for the constant determination is derived for the mean-shifted binary hypothesis testing problem

The generalized likelihood ratio test (GLRT) is a standard tool for designing signal detectors. It produces detectors that perform well when the signal model is known, except for a fixed set of signal parameters. However, it is unable to accommodate multiple signal models. We introduce the multifamily likelihood ratio test, which extends the GLRT and alleviates this limitation.

Estimation of the phase of a sinusoid is an important problem in signal processing. The usual maximum likelihood estimator is biased and so can produce poor results, especially at low signal-to-noise ratios and/or short data records. It is proven that no unbiased estimator exists; based on the proof, several means of obtaining estimators with less bias than the maximum likelihood estimator are proposed.

The paper describes a vector space approach to solving the multidimensional (mD) Yule-Walker equations for an arbitrary region of support. This approach leads to a solution that is simple to implement. Two-dimensional (2D) autoregressive (AR) modelling has found applications in image processing, sonar, and other areas. 3D and higher dimensional AR modelling has as yet to be extensively studied but applications to signals that vary in time, frequency, and space can easily be envisioned.

The generalized likelihood ratio test (GLRT) is invariant with respect to transformations for which the hypothesis testing problem itself is invariant. This result from the statistics literature is presented in the context of some simple signal models. This is an important property of the GLRT in light of its widespread use and the recent interest in invariant tests applied to signal processing applications. The GLRT is derived for some examples in which the uniformly most powerful invariant (UMPI) test does and does not exist, including one in which the UMPI test exists and is not given by the GLRT.

This work is concerned with the optimization of an active sonar or radar transmit signal, to maximize the probability of detecting a nonmoving point target in the presence of signal-dependent reverberation and colored ambient noise whose power spectral densities are known. An analytical solution first reported by Kooij is corrected and extended. A simple example for the white ambient noise case is included to provide insight into the transmit signal optimization. This example shows that the effect of the solution is to “pre-emphasize” the transmit signal, which results in the whitening of the signal-dependent reverberation power spectral density.

We address the problem of parameter estimation of superimposed chirp signals in noise. The approach used here is a computationally modest implementation of a maximum likelihood (ML) technique. The ML technique for estimating the complex amplitudes, chirping rates and frequencies reduces to a separable optimization problem where the chirping rates and frequencies are determined by maximizing a compressed likelihood function which is a function of only the chirping rates and frequencies. Since the compressed likelihood function is multidimensional, its maximization via grid search is impractical. We propose a non-iterative maximization of the compressed likelihood. function using importance sampling. Simulation results are presented for a scenario involving closely spaced parameters for the individual signals.

It is shown that under certain conditions the performance of a suboptimal detector may be improved by adding noise to the received data. The reasons for this counterintuitive result are explained and a computer simulation example given.

A new proof of the class-specific feature theorem is given. The proof makes use of the observed data as opposed to the set of sufficient statistics as in the original formulation. We prove the theorem for the classical case, in which the parameter vector is deterministic and known, as well as for the Bayesian case, in which the parameter vector is modeled as a random vector with known prior probability density function. The essence of the theorem is that with a suitable normalization the probability density function of the sufficient statistic for each probability density function family can be used for optimal classification. One need not have knowledge of the probability density functions of the data under each hypothesis.

Noting that the probability density function of a continuous random variable has similar properties to a power spectral density, a new class of probability density function estimators is described. The specific model examined is the autoregressive model, although the extension to other time series models is evident. An example is given to illustrate the approach.

This paper considers a method for estimating time delays, amplitudes, and Doppler scales of a multipath signal. The method is an extension of work previously reported by Manickam and Vaccaro (1993) which dealt solely with time delays and amplitudes, and extended by Habboosh and Vaccaro (see Proceedings CISS '96, p.633-8, 1996) to include Doppler scale. An algorithm is presented for determining the size of the indicator set to reduce ill-conditioning of the signal subspace matrix. Simulation results are shown and comparisons to the Cramer-Rao lower bound provided; these results show that significant reduction in estimate variances can be achieved using the deconvolution approach with a properly selected indicator set.

This paper presents a system for separating the cochannel speech of two talkers. The proposed harmonic enhancement and suppression (HES) system is based on a frame-by-frame speaker separation algorithm that exploits the pitch estimate of the stronger talker derived from the cochannel signal. The idea behind this approach is to recover the stronger talker's speech by enhancing their harmonic frequencies and formants given a multiresolution pitch estimate. The weaker talker's speech is obtained from the residual signal created when the harmonics and formants of the stronger talker are suppressed. An automatic speaker assignment algorithm is used to place recovered frames from the target and interfering talkers in separate channels. Automatic speaker assignment performs reasonably well in most cochannel environments, including voiced-on-voiced, voiced-on-unvoiced, unvoiced-on-unvoiced, assignment after processing silence intervals, and single talker speech (no cochannel interference). The HES system has been tested at target-to-interferer ratios (TIRs) from -18 to 18 dB with widely available data bases. It has demonstrated improved performance in keyword spotting tests for TIR values of 6, 12, and 18 dB, and in human listening tests for TIR values of -6 and -18 dB.

We show how to realize one-dimensional chaotic signals with the given first order autoregressive (AR(1)) autocorrelation function (ACF) of the form r[k]=r[0]a/sup k/, where 0<a<1. We consider the class of piecewise linear and "piecewise onto" maps defined from the unit interval [0,1] onto itself. We prove that these maps are chaotic using their topological conjugacy with known chaotic maps. The autocovariance function of sequences generated by these maps can be calculated analytically as an ensemble average. The expression for the autocovariance function leads to a way of designing chaotic signals with the given ACF. ACF estimates (temporal averages) of typical signals are close to the theoretical values (ensemble averages).

A method for determining the frequency of a real sinusoid is proposed. Based on exponential sampling of the waveform, the approach requires virtually no computation. It can be easily implemented in digital hardware.>

A very useful and not too restrictive class of models of nonstationary signals is based upon the assumptions that the signals are composed of independent and stationary segments that can be represented by autoregressive models. A usual task is then to find the number of segments of the observed signal, their boundaries, and the best model for each segment. A Bayesian solution to this task is proposed which does not require setting of any thresholds. The technical implementation of the solution is carried out via dynamic programming. The Monte Carlo simulations show excellent results.>

Parameter estimation for a periodic signal in colored noise of unknown power spectral density is examined. The estimator is based on the minimum descriptive length criterion and maximum likelihood theory developed for the CARD model. Computer simulations to demonstrate the excellent performance of the proposed estimator are included.>

The problem of signal separation for nonlinear dynamical systems, particularly chaotic systems, is considered. These systems are characterized by a stretching and folding within state space and by the presence of an attractor. Signal separation involves the separation of a received signal into two components, one of which is modeled as the output of a nonlinear dynamical system. The authors review previous approaches to this problem and present results from the application of Kalman filtering to the signal separation problem. A Cramer-Rao bound on the performance of a signal separation algorithm in white noise is presented. The special properties of nonlinear dynamical systems allow state estimation that improves exponentially with the number of observations but requires special processing techniques to achieve.>

A generalized likelihood ratio test is described to detect a single transient signal in an unknown colored noise field using a line array. The transient signal is a one-sided exponential with known mode but unknown arrival angle and arrival time. Vast improvements over a conventional energy-based detector are possible and are attributed to prewhitening to account for the noise coloration.>

The work on model order estimation by Bayesian predictive densities of 1-D real autoregressive processes is extended to 2-D complex autoregressive processes. According to the procedure, the best model is the one which most accurately predicts the data yet to be observed and whose parameters are estimated from the data already observed. The derivation steps of the algorithm are demonstrated and verified by computer simulations. The computer simulations show that the algorithm based on this approach yields good results.>

Time series modeling as the sum of an autoregressive (AR) process and sinusoids is proposed. When the AR model order is infinite, it is called the canonical autoregressive decomposition and is equivalent to the Wold decomposition. Maximum likelihood estimation of the sinusoidal and AR parameters is shown to require minimization with respect to only the unknown frequencies. Although the estimation problem is nonlinear in the sinusoidal amplitudes and AR parameters, it is reduced to a linear least-squares problem by using a nonlinear parameter transformation. Similar results are derived for AR processes in polynomial or polynomial-times-exponential signals. Applications include frequency estimation/transient analysis in unknown colored noise.>

A model selection criterion based on Bayesian predictive densities is derived. Starting with an improper prior distribution of the model parameters and using one portion of the data, a proper distribution is obtained which is further used as a prior for obtaining predictive densities according to the model and the first portion of the data. The remaining portion is used to validate the model through the obtained predictive densities. The procedure is applied to the set of linear regression models. The performance of the criterion is illustrated by simulation results.>

Frequency-rate estimation of a linearly frequency modulated signal is addressed. A simple estimation procedure that yields accurate estimates for moderately high signal-to-noise ratios is proposed. By transforming the original sequence into a sequence that is the phase data differenced twice, the problem becomes equivalent to estimating a constant in colored noise. Computer simulations verify the expected performance and show that the estimator achieves the Cramer-Rao bound for signal-to-noise ratios above 8 dB.>

A formalism for frequency estimation of multiple sinusoids in noise using dynamic programming is derived. A dynamic-programming-type algorithm for the frequency estimation of two close sinusoids in noise is proposed. Computer simulation results show an improvement over the periodogram.>

A frequency estimator for a single complex sinusoid in complex white Gaussian noise is proposed. The estimator is more computationally efficient that the optimal maximum-likelihood estimator yet attains as good performance at moderately high signal-to-noise ratios. Also, the estimator is shown to be related to the linear prediction estimator. This relationship is exploited to reveal why the linear prediction estimator does not attain the Cramer-Rao bound even at high signal-to-noise ratios.>

An approximate maximum-likelihood estimator is derived for ARMA (autoregressive moving-average) processes and is shown to correspond to least-squares fitting of the estimated cepstrum of the process by the model cepstrum. Experiments with several simple ARMA

A new technique for the estimation of autoregressive filter parameters of a non-Gaussian autoregressive process is proposed. The probability density function of the driving noise is assumed to be known. The new technique is a two-stage procedure motivated by maximum likelihood estimation. It is computationally much simpler than the maximum likelihood estimator and does not suffer from convergence prroblems. Computer simulations indicate that unlike the least squares or linear prediction estimators, the proposed estimator is nearly eifficient, even for moderately Sized data records.

The problem of detecting a signal known except for amplitude in incompletely characterized non-Gaussian noise is addressed. The use of a generalized likelihood ratio test or its asymptotically equivalent form, the Rao test, is shown to produce a detector that has the identical asymptotic performance as a generalized likelihood ratio test designed with a priori knowledge of the unknown noise parameters. Since the latter clairvoyant detector always produces an upper bound on performance, the generalized likelihood ratio test is optimum. An example is given in which the noise is modeled as an autoregressive process with a mixed-Gaussian noise excitation. Results of a computer simulation are described which verify the theory.

The problem of detection of a broadband wide sense stationary Gaussian signal of unknown power spectral density in white Gaussian noise is addressed. By modeling the signal in noise as an autoregressive process a generalized likelihood ratio test is formulated for the parameters of the autoregressive process. It is shown that the proposed detector outperforms the conventional energy detector. The gain in performance is greatest when the autoregressive model order is small.

A variety of methods have been proposed for the detection of a signal, with unknown signal parameters, in a noisy environment. In this paper, the noise statistics are incorporated to reveal that certain processing of the Wigner distribution (WD) signal representation can lead to an optimal, and often easy to compute, detection scheme. For the special case of linear FM signals in complex white Gaussian noise, it is shown that the optimal detector is equivalent to integrating the WD along the line of instantaneous frequency. If the position and sweep rate of the linear chirp are unknown, then a Generalized Likelihood Ratio Test (GLRT) leads one to integrate the WD along all possible lines in the time-frequency plane and choose the largest integrated value for comparison to a threshold. Simulation examples of the WD detection scheme are given to demonstrate the utility of the proposed method. Finally, some comments concerning the detection of the general phase modulated signal are offered.

An edge detector based on the linear model is developed which utilizes the generalized likelihood ratio for statistical hypothesis testing. The performance of this detector is analytically and experimentally compared to that of a gradient operator (Sobel) and is shown to have a slightly higher detection rate for a given false alarm rate. The detector is also invariant to multiplicative changes of the gray-scale values of the image.

A large class of physical signals may be characterized by mode parameters (natural frequencies and damping coefficients) and initial conditions. The mode parameters, usually governed by well understood physical models, are often accurately known apriori. Conversely, very little is usually known about initial conditions. The problem of interest here is to detect signals with known modes, but unknown initial conditions, in additive Gaussian noise of unknown level. The signals may also be characterized as impulse responses of ARMA systems with unknown MA parts. We derive an F-statistic that is optimum (uniformly most powerful) in the class of all receivers that are invariant to certain tranformations of the data. We argue that the invariances are natural constraints. The statistic we derive provides constant false alarm rate performance.

Conventional narrowband detectors suffer large losses in detection performance when the assumed sinusoidal receive signal is actually frequency modulated. Such would be the case for the detection of a maneuvering target by a passive sonar system. Based upon autoregressive spectral analysis a detector is presented which is nearly invariant to frequency modulation. In fact, for a large enough frequency modulation the autoregressive detector yields about a 4 dB improvement in detection performance over the conventional narrow-band detector. Furthermore, the autoregressive detector is a CFAR receiver and requires less computation and storage than a conventional narrow-band detector. Thus, the autoregressive detector should be an attractive complement to a conventional narrowband detector.

The problem of detecting a sinusoid of unknown frequency and random phase in white noise is essentially a problem in spectral analysis. The conventional approach is to utilize a Periodogram. This paper examines the merits of a detector based on the auto-regressive spectral estimator. Some advantages of the autoregressive detector are that the performance is independent of the unknown frequency, and the false alarm rate is independent of the noise level. Also, for the first order AR model investigated, the computational and storage requirements needed to compute the test statistic are less than those of the Periodogram. The performance of the AR detector with a model order of one is, however, inferior to that of the Periodogram.

The Fourier-Autoregressive spectral estimator allows one to perform autoregressive spectral estimation on a narrowband basis as opposed to the conventional broadband approach. This capability is particularly valuable when the desired time series is a narrowband process, which is embedded in broadband observation noise. To generate the narrowband time series, the original data is passed through a bank of bandpass filters which is conveniently implemented by an FFT. It is shown that for a sinusoidal process in white noise, a tradeoff may be effected between the narrowband signal-to-noise ratio, which is principally responsible for spectral resolution, and the useable data record length.

Spectral line splitting in autoregressive spectral estimation changes what should be a single spectral line into two or more displaced spectral lines. Fougere was the first researcher to note the existence of certain conditions for sinusoidal data for which splitting occurred. He proposed a complicated gradient-descent algorithm which seems to fix the problem for at least one sinusoid. It is shown that spectral line splitting is a result of estimation errors and is not inherent in the autoregressive approach. In particular, the interaction between positive and negative sinusoidal frequency components in the Burg reflection coefficient and Yule-Walker auto-correlation estimates and the use of the biased autocorrelation estimator in the Yule-Walker approach is responsible for spectral line splitting. Spectral line splitting may be alleviated for one sinusoid by using complex data and also, the unbiased autocorrelation estimator in the Yule-Walker case. Spectral line splitting for multiple sinusoids is discussed.

The autoregressive (maximum entropy, linear prediction) power spectral density estimator has been shown to possess excellent resolution properties. However, the addition of noise to the time series under analysis may drastically alter the spectral estimate. To reduce the effects of noise, an adaptive filtering algorithm is proposed that is directly applicable to sinusoidal signals in white noise. Its use for more general signals is discussed.